Colombo–Katunayake Expressway (CKE) is the second major highway in Sri Lanka connecting the International Airport at Katunayake to Colombo, and this expressway is constructed over soft soils, predominantly peat. A research study was conducted to analyse the stability of two critical sections of the CKE project using finite element method (FEM), limit equilibrium method (LEM) and Matsuo chart. In the FEM, PLAXIS 2D package was used to simulate the behaviour by using four different types of analyses: (1) Mohr–Coulomb (MC) analysis: MC model for all soil layers; (2) MC-SS 1 analysis: soft soil (SS) model for peat and MC model for remaining soil layers; (3) MC-SS 2 analysis: SS model for peat and soft clay layers and MC model for remaining soil layers; and (4) MC-SS-SSC analysis: soft soil creep (SSC) model for peat, SS model for soft clay and MC model for remaining soil layers. Further, LEM analysis was carried out using SLOPE/W and obtained factor of safety (FOS) values were compared with the FEM analysis. In addition, effect of geotextile on the long-term stability was analysed in FEM. Based on the outcome of the FEM analysis, it was noticed that MC-SS 2 model is the best model to predict the actual field condition for soft soil with high overconsolidation ratio values. In addition, FOS values obtained from PLAXIS were in very good agreement with those obtained from SLOPE/W. Incorporation of geotextile improves the stability of the embankment, and the optimum stiffness of the geotextile should be selected for practical applications.